Question: Ashley is 6 years older than Christopher. Nine years ago, Ashley was 4 times as old as Christopher. How old is Christopher now?
Solution: We can use the given information to write down two equations that describe the ages of Ashley and Christopher. Let Ashley's current age be $a$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $a = c + 6$ Nine years ago, Ashley was $a - 9$ years old, and Christopher was $c - 9$ years old. The information in the second sentence can be expressed in the following equation: $a - 9 = 4(c - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $c$ , it might be easiest to use our first equation for $a$ and substitute it into our second equation. Our first equation is: $a = c + 6$ . Substituting this into our second equation, we get the equation: $(c + 6)$ $-$ $9 = 4(c - 9)$ which combines the information about $c$ from both of our original equations. Simplifying both sides of this equation, we get: $c - 3 = 4 c - 36$ Solving for $c$ , we get: $3 c = 33$ $c = 11$.